Evaluation of the mode I plastic zone size at the crack tip using RKPM and FEM

Abstract

In recent years, much research have been done on mesh-free methods for solving differential equation problems including crack and also obtained satisfactory results. Among these methods Reproducing Kernel Particle Method (RKPM) has been used increasingly in fracture mechanic problems. RKPM is a meshfree technology which has proven very useful for solving problems of fracture mechanics. In this study, it is proposed to obtain the mode I plastic zone size and shape at the crack-tip in a work-hardening material using RKPM. Ramberg-Osgood stress-strain relation is assumed. Results including plastic zone shape are compared with finite element method (FEM) to show the accuracy of RKPM. Results show that the plastic zone size in crack tip for the plane-strain condition is bigger that plane-stress condition. The reason can be stated that in plane-strain condition due to limitations in third dimension, stress is created in the third dimension (z-direction) and cause to increase the daviatoric stress according to J2-Deformational theory and also cause to increase in plastic zone size. The main objective is to obtain the mode I plastic zone shape at the crack-tip in a work-hardening material using RKPM and FEM.